A Key to the Exercises and Examples Contained in a Text-book of Euclid's ElementsMacmillan, 1892 - 147 |
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Strona vii
... constant . " For Ex . 39 read , " Given the base and vertical angle of a triangle , find the locus of the centre of the circle which passes through the three escribed centres . " Page 284. In place of Ex . 13 read , " Given the ...
... constant . " For Ex . 39 read , " Given the base and vertical angle of a triangle , find the locus of the centre of the circle which passes through the three escribed centres . " Page 284. In place of Ex . 13 read , " Given the ...
Strona 30
... constant , being equal to half of AB . Thus the locus is a circle whose centre is D and radius equal to half the given base . 9. Bisect AB in C and AX in D and join DC . Then the locus required is the locus of the vertices of right ...
... constant , being equal to half of AB . Thus the locus is a circle whose centre is D and radius equal to half the given base . 9. Bisect AB in C and AX in D and join DC . Then the locus required is the locus of the vertices of right ...
Strona 31
... constant , A must move on a fixed st . line par1 . to BC . Let AX be the median bisecting BC ; then if o is the inters " . of medians AO = 20X [ Ex . 4 , p . 105 ] . Draw AD perp . to BC and in it take AP = 2PD [ Ex . 19 , p . 99 ] ...
... constant , A must move on a fixed st . line par1 . to BC . Let AX be the median bisecting BC ; then if o is the inters " . of medians AO = 20X [ Ex . 4 , p . 105 ] . Draw AD perp . to BC and in it take AP = 2PD [ Ex . 19 , p . 99 ] ...
Strona 41
... constant , .. AP2 + BP2 is constant . 30. Let BC be the base , and ABC the A in one of its positions . Bisect BC at X , and join AX . Then BA2 + AC2 = 2 ( BX2 + AX2 ) [ Ex . 24 , p . 147 ] . But BA2 + AC2 is constant by hyp . .. BX2 + ...
... constant , .. AP2 + BP2 is constant . 30. Let BC be the base , and ABC the A in one of its positions . Bisect BC at X , and join AX . Then BA2 + AC2 = 2 ( BX2 + AX2 ) [ Ex . 24 , p . 147 ] . But BA2 + AC2 is constant by hyp . .. BX2 + ...
Strona 49
... constant . Page 175 . Draw the Draw 1. Let A be the given pt . , and B the centre . chord CAD perp . to AB , and any other chord EAF through A. BG perp . to EF . Then the hypotenuse BA > BG . .. chord CD chord EF ; that is , CD is the ...
... constant . Page 175 . Draw the Draw 1. Let A be the given pt . , and B the centre . chord CAD perp . to AB , and any other chord EAF through A. BG perp . to EF . Then the hypotenuse BA > BG . .. chord CD chord EF ; that is , CD is the ...
Inne wydania - Wyświetl wszystko
A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H S 1848-1934 Hall Podgląd niedostępny - 2018 |
A Key to the Exercises and Examples Contained in a Text-Book of Euclid's ... H. S. Hall Podgląd niedostępny - 2017 |
Kluczowe wyrazy i wyrażenia
A. W. VERRALL AABC AB² ABCD AC² angles Assistant Master AX² BC² bisector bisects Cambridge centre chord circle circum College concyclic constant describe diam diameter diff draw ELEMENTARY equiangular equilat FASNACHT Fcap fixed point G. E. FASNACHT given base given point given ratio given st GREEK Hence identically equal inscribed intersect Introduction and Notes ISAAC TODHUNTER isosceles Join Let ABC LL.D locus M.A. BOOK meet middle point middle pt orthocentre Owens College par¹ parm pedal triangle perp plane produced Prof Professor Radical Axis radius equal rect respectively segment shewn sides Similarly sum of sqq tangent touch Translated triangle Trinity College vert vols
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